Estimates for Sobolev-orthonormal functions and generated by Laguerre functions

In this paper, we consider the system of functions $\lambda_{r,n}^\alpha(x)$ $(n=0, 1,\ldots)$, $\alpha>-1$, $r\in\mathbb{N}$, orthonormal with respect to a Sobolev-type inner product and generated by the system of Laguerre functions. Using asymptotic formulas for the Laguerre polynomials, we obtain estimates for functions $\lambda_{r,n}^\alpha(x)$, $x\in[0, \infty)$.